Question: Nala is escaping from the dragon's lair! She is running toward the entrance of the lair at a speed of $9.2$ meters per second. The entrance is $180$ meters away. The distance $d$ between Nala and the entrance of the lair is a function of $t$, the time in seconds since Nala began running. Write the function's formula. $d=$
Solution: Nala's speed is constant, so we're dealing with a linear relationship. We could write the desired formula in slope-intercept form: $d= mt+ b$. In this form, $ m$ gives us the slope of the graph of the function and $ b$ gives us the $y$ -intercept. Our goal is to find the values of $ m$ and $ b$ and substitute them into this formula. We know that for each second Nala runs, the distance between her and the entrance decreases by $9.2$ meters, so the slope $ m$ is ${-9.2}$, and our function looks like $d={-9.2}t+ b$. We also know that Nala is $180$ meters away from the entrance initially, so the $y$ -intercept ${b}$ is ${180}$. Since ${m}={-9.2}$ and ${b}={180}$, the desired formula is: $d={-9.2}t+{180}$